Solve A_4^2*A_4^3*A_4^3

$$A _ { 4 } ^ { 2 } \times A _ { 4 } ^ { 3 } \times A _ { 4 } ^ { 3 }$$

Evaluate

$$A_{4}^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$A_{4}^{2}A_{4}^{3}A_{4}^{3}$$

Use the Multiplication Rule for Exponents.

$$A_{4}^{2+3+3}$$

Add the exponents 2 and 3.

$$A_{4}^{5+3}$$

Add the exponents 5 and 3.

$$A_{4}^{8}$$

Differentiate w.r.t. A_4

$$8A_{4}^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}A_{4}}(A_{4}^{5}A_{4}^{3})$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}A_{4}}(A_{4}^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8A_{4}^{8-1}$$

Subtract 1 from 8.

$$8A_{4}^{7}$$